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Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
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Rigid Body Equilibrium Problems - II01:21

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A rigid body is in static equilibrium when the net force and the net torque acting on the system are equal to zero.
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The total angular momentum of a rigid body can be calculated using the summation of the angular momentum of all the tiny particles rotating in the same plane. Considering all the tiny particles rotating in the x-y plane, the direction of angular momentum of all such particles and that of the rigid body would be perpendicular to the plane of the rotation along the z-axis.
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The movement of a rigid object can be understood through the equations that explain both translational and rotational motion about the center of mass of the object, point G. This center of mass is the point where the equation of motion for translational motion comes into play, as per Newton's Second Law.
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Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
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A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction.

E M Kolahdouz1,2, A P S Bhalla3, L N Scotten4

  • 1Division of Applied Mechanics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, United States Food and Drug Administration, Silver Spring, MD, USA.

Journal of Computational Physics
|June 21, 2021
PubMed
Summary
This summary is machine-generated.

This study presents a novel immersed Lagrangian-Eulerian (ILE) method for simulating fluid-structure interaction (FSI) with rigid bodies in viscous fluids. The ILE method ensures stability across various density ratios and is applied to biomedical FSI cases.

Keywords:
Fluid-structure interactionclot transportimmersed interface methodimmersed methodsinferior vena cavalow density ratiosmechanical heart valverigid body dynamics

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Area of Science:

  • Computational Fluid Dynamics
  • Biomedical Engineering
  • Numerical Methods

Background:

  • Simulating fluid-structure interaction (FSI) is crucial for understanding complex phenomena in engineering and medicine.
  • Existing methods often face challenges with stability, particularly concerning the added mass effect and varying density ratios.
  • Accurate modeling of rigid bodies immersed in viscous incompressible fluids requires robust numerical techniques.

Purpose of the Study:

  • To introduce and validate a novel sharp interface method for fluid-structure interaction (FSI) simulations.
  • To develop an immersed Lagrangian-Eulerian (ILE) approach integrating partitioned and immersed FSI formulation aspects.
  • To demonstrate the method's capability in handling large-scale biomedical FSI problems.

Main Methods:

  • Developed an immersed Lagrangian-Eulerian (ILE) method solving separate fluid and solid momentum equations.
  • Employed non-conforming discretizations for fluid and structure regions with a Dirichlet-Neumann coupling scheme.
  • Utilized a penalty approach and immersed interface method (IIM) to enforce the no-slip condition and accurately compute interface stresses.

Main Results:

  • The ILE method demonstrated stability across a wide range of solid-fluid density ratios, including extreme cases.
  • Benchmarking with various test cases confirmed the methodology's accuracy and robustness.
  • Successful application to large-scale biomedical FSI simulations, including heart valve dynamics and blood clot transport.

Conclusions:

  • The proposed immersed Lagrangian-Eulerian (ILE) method provides a stable and accurate approach for simulating FSI involving immersed rigid bodies.
  • The technique effectively handles complex interfaces and varying density ratios, overcoming limitations of traditional methods.
  • This methodology holds significant potential for advancing research in biomedical fluid dynamics and device design.